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Remove the rectangle ABEF from the square ABCD , and remove the rectangle DHGF from the rectangle ECDF , if the area of ABEF and.. DHGF are equal.Find the area of square ABCD.[r]
(1)2018 WMTC 儿童组个人赛第一轮
Junior Level Individual Round 1
1 Known sequence:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …，starting with three numbers, each number equals the sum of its two preceding ones How many odd numbers are there in the first 2018 numbers?
2 If (1) x y z, , are different from each other and they are one of 3, 5, 7, respectively
(2) xyz is a three digits number, 2018xyz is the multiple of
(3)2018xyz a b c ，a b c, , are the sides of a triangle Find the length of largest side of this triangle
3 Plant trees on both sides of a road, if the distance of any two adjacent trees is meters, there will be trees left; if the distance is meters, 73 trees will be needed.The length of this road is meters
4 The 28 students in Class A went to the library There are 32 girls in this Class, the girls in this class who didn’t go to the library wasM, and the boy in this class who go to the library wasN FindM-N.
5 M is a two digits number, 5 M 851
M
is a reducible fraction Find
the maximum value ofM
(2)6 In square ABCD, the area of triangle BGE is 2000, the area of triangleBGFis 400 Find EF×BG
7 The rectangular ABCD is divided into different small rectangles The number in the figure is the circumference of the small rectangles in which it located FindAB+BC+CD+DA
8 In trapezoid ABCD, the sides of ABCD is adjustable, but always satisfy : AB∥CD, AB<CD, ifACandBD intersect at pointO How many
(3)2018 WMTC 儿童组个人赛第二轮
Junior Level Individual Round 2
9 If x 1x x
，find value of
1 1 1 2 2017 2018
2018 2017
10 The three digits abc is a prime number, and a+b+c=14, if useA
andB to represent its maximum and minimum value, then A+B= 11 Remove the rectangle ABEF from the square ABCD, and remove the rectangle DHGF from the rectangle ECDF, if the area of ABEF and
DHGF are equal.Find the area of squareABCD
12 In rectangular ABCD, AD1 ， 1
AD AD ， 2 1
AD AD ，
3
3
AD AD ，…， 1
n n n
AD AD n ；
AB ， 1
AB AB， 2 1
AB AB ，
3
4
AB AB ，…， 1
n n n
AB AB n
if the area of AB C D1 1，AB C D2 2，… are
S , S2,…, respectively, the value of S S1 2S3 S10 is
(4)2018 WMTC 儿童组个人赛第三轮
Junior Level Individual Round 3
13.3,4,5,6,7 are five continuous natural numbers 3+4+5+6+7=25=52, it is a square number Ask how many arrays like (3,4,5,6,7) within 100?
14 The area of the square ABCD is 40, BE13AB, and
5
BF BC
Find the area of quadrilateralBGHF
(5)2018 WMTC 儿童组接力赛第一轮
Junior Level Relay Round 1
1-A
There are N people attend a meeting Everyone should shake hands with the others If the total number of shake hands is 45 FindN
(6)2018 WMTC 儿童组接力赛第一轮
Junior Level Relay Round 1
1-B LetT be the number you will receive
Now, age of my uncle is times of mine And T years later, my age equal to my uncle’s ageT years ago How old is my uncle now?
(7)2018 WMTC 儿童组接力赛第二轮
Junior Level Relay Round 2
2-A Ifa,b,care prime numbers, and a2b2c2 150
, Find a b c .
(8)2018 WMTC 儿童组接力赛第二轮
Junior Level Relay Round 2
2-B LetT be the number you will receive
In the rectangle ABCD , EF∥AB, GH∥DA, EF andGH intersect at point O, EF andCH intersect at point I, and AH:HB=AE:ED=1:3, area of triangleCOI isT Find the area of rectangle ABCD
(9)2018 WMTC 儿童组接力赛第三轮
Junior Level Relay Round 3
3-A
If C2 A2 B2, and C2 is a three digits number Find the maximum
value of C2
(10)2018 WMTC 儿童组接力赛第三轮
Junior Level Relay Round 3
3-B LetT be the number you will receive In the triangle ABC, DC 14BC,
3
FC AC , area of triangle ABC is
T Find the area of triangleDCF
(11)2018 WMTC 儿童组团体赛
Junior Level Team Round
1 If 2020 2020 20182019 2019 n
m
is a simplest fraction, then m+n=
2 When number A divided by 2, the remainder is When it is divided by 5, the remainder is When it is divided by 10, the remainder is
3 55 same cubes are stacked as shown in Fig.1 Now color the surface（under face is not included） of the whole polyhedron The number of cubes that are not colored is
Fig.1
4 x represents the decimal part of x, then
2018 2018 2018 2018 2018
5 5
=
5 If x and y are prime numbers, and x+y=60 How many pairs of （x,y） are there?
(12)6 In the following graph, there are a big circle and four identical small circles, the diameter of the small circle is 10 Find the area of the shadow.（π=3.14）
7 Make a big rectangle by 12 small rectangles with no overlap How many different value of perimeter of the big rectangle?
8 The three digits number abc can be divisible by 35, and
a+b+c=12 How many abc are there?
9 How many odd numbers can 2,0,1 and composed?(you can just use several of them and every digit can be used once at a time)
10 In the trapezoidal ABCD, ∠D=∠C=90°, AD=6,BC=12,DC=24
M is the midpoint of AB, point N on CD, MN divide the area of ABCD
into two equal part FindDN
(13)12 In triangle ABC, ∠A=90°, AB=AC, BC=4, take point A as the center of the circle, and the height of the edge BC as the radius draw the arc, it intersect edges AB, AC and CB at point D,E,M And take the point
C as the center of the circle and take the length of AC as the radius, draw arc, intersect CB at point F S1,S2 are different shadow as shown in the Fig.Find S S1 2.(use π=3)
13 p p p1, , , p2018 are prime numbers more than 100 If
N= 2
1 2018
p p p When Nis divided by 3,what is the remainder?
（p2 p p）
14 Suppose abc is a three digits number, and abc ab bc ca ， then a b c ＝
15 ABCDEF is a regular hexagon with length 150 meters Paul and Jeanne at the same time starting fromAandF respectively and walking in the same direction, Jeanne is behind Paul, the speed of Paul is 50 m/min The speed of Jeanne is 40 m/min When they walk on the same side of
(14)16 The square EFGH is inside the square ABCD The difference of their area is 200.Point E,H on AD, point O is the midpoint of CF The area ofBOGF=
17 Point E,F,G,H on sides of square ABCD,the perpendiculars from these four points to the edges of the ABCD form a rectangle (4×2), If
AB=10, then area ofEFGH =
18 abc is a three digits number, it is a multiple of 36 If abc bac =180 Then maximum of abc is
19 N is the multiple of 5, when divided by 6, the remainder is 1; when divided by 8, the remainder is The minimum ofNis
(15)2018WMTC Junior Level Individual Rounds
1 2 3 4 5 6 7
1346 17 800 99 3200 40
8 9 10 11 12 13 14
5 20171
2 1090 144
5
12
Relay Rounds
Team Round
1 2 3 4 5 6 7 8 9 10
1347 14 807 12 57 11 16
11 12 13 14 15 16 17 18 19 20
481或
592 0.5 2 63 50 46 972 115 720
1-B 2-B 3-B